MATHEMATICS

y
(x, y)
5
O
Figure 5.11
(x 1
, y 1
)
The gradient, m, of the line joining (x 1
, y 1
) to (x, y) is given by
y
−
y
1
m
=
x
−
x
1
➝ y − y mx ( x
)
1
= −
1
For example, the equation of the line with gradient 2 that passes through the
point (3, −1) can be written as y − ( − 1) = 2( x − 3)
which can be simplified to y
x
= 2x
− 7.
(ii) Given the gradient, m, and the y-intercept (0, c)
A special case of y − y1 = mx ( − x1)
is
when (x 1
, y 1
) is the y-intercept (0, c).
This is a very useful form of the
equation of a straight line.
y = mx + c
The equation then becomes
Substituting x1 0
y = mx + c
y
= and
1
= c into the equation
as shown in Figure 5.12.
When the line passes through the origin, the equation is
y = mx
The y-intercept is (0, 0), so c = 0
as shown in Figure 5.13.
Chapter 5 Coordinate geometry
y
y
y = mx + c
y = mx
(0, c)
O
x
O
x
Figure 5.12
Figure 5.13
11